A new estimator for information dimension with standard errors and confidence intervals

A new least-squares approach to information dimension estimation of the invariant distribution of a dynamical system is suggested. It is computationally similar to the Grassberger-Procaccia algorithm for estimating the correlation dimension over a fixed range of radii. Under mixing assumptions on the observations that are customary for chaotic dynamical systems, the estimator enjoys nearly the same asymptotic normality properties as the Grassberger-Procaccia procedure. Technically, one has to deal with a mixture of U- and L-statistic representations and their modifications for data from deterministic chaotic dynamical systems to estimate smoothly trimmed spatial correlation integrals.